SOLUTION: A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by a b = 5-inch arm at the center of the base of the window, as shown in the figu

Algebra ->  Trigonometry-basics -> SOLUTION: A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by a b = 5-inch arm at the center of the base of the window, as shown in the figu      Log On


   

Question 832030: A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by a b = 5-inch arm at the center of the base of the window, as shown in the figure below. If the arm rotates 120°, approximate the percentage of the window's area that is wiped by the blade. (Round your answer to one decimal place.)
Answer by math-vortex(648) About Me  (Show Source):
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Hi, there--

THE PROBLEM:
A rectangular window measures 54 inches by 24 inches. There is an a = 14-inch wiper blade attached by 
a b = 5-inch arm at the center of the base of the window, as shown in the figure below. If the arm rotates 
120°, approximate the percentage of the window's area that is wiped by the blade. (Round your answer to 
one decimal place.)

A SOLUTION:

Find the area of the rectangle window.
Let L be the length of the window.
Let W be the width.

The area is length times width, 54 * 24 = 1296 square inches.

Find the area of window swept by wipers.
The radius of the wiper is 14 inches. It wipes 120 degrees. This is one-third of a circle because 
120/360 = 1/3

The area of one-third of the circle is %28pi%2Ar%5E2%29%2F3=%28196%2Api%29%2F3

We want the percentage of the window that is swept by the wiper.

[area swept by wiper] / [area of window] * 100 = [percentage of window area swept by wiper]
%28%28%28196%2Api%29%2F3%29%2F1296%29%2A100=15.8 percent.


Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com